The vector A has x, y, and z components of 8, 12, and 24 units, respectively. a) Write a vector expression for A in unit-vector notation. b) Obtain a unit-vector expression for a vector B one-fourth the length of A pointing in the same direction as A. c) Obtain a unit-vector expression for a vector C three times the length of A pointing in the direction opposite the direction of A.

Q: Let u = a1i + b1 j, v = a2 i + b2 j, w = a3 i + b3 j. Prove the given property by obtaining the…

A:

Q: Find a unit vector (a) in the direction of v and (b) in the direction opposite of v. v = 4i − 5j +…

A: Now magnitude of v is,

Q: Determine the two unit vectors that are orthogonal to A= . Which two unit vectors are parallel to A?

A: Given that, A = <1, 2> Suppose that <a, b> is orthogonal to the vector A = <1, 2>…

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i +j and i- 6j as…

A: Here we have to find the length of the diagonal.

Q: Find the value of a so that vectors U = ai + 3j and V = 9i + 9j are perpendicular. a =

A: Given: U=ai+3jV=9i+9jθ=90ο

Q: Find a vector v such that ||v|| = 20 and v is in the same direction as 15i + 15j

A:

Q: Find a vector v such that v = 15 and v is in the same direction as –li + 13j

A: The solution is given as

Q: Find the components of the vectors u, v, u + v, and u - v, where u and v are as shown in Figure.

A: Given:

Q: Use the accompanying figure to write each vector listed in Exer- cises 7 and 8 as a linear…

A: Given - Use the accompanying figure to write each vector listed in Exercise 8 as a linear…

Q: For the vector arrangement presented determine: -Express each vector on its cartesian form.…

A:

Q: Find the angle between the diagonals of a parallelogram constructed on the vectors a=2 i +j and b=-2…

A:

Q: [:] [] Find c so that the vectors and are parallel.

A: Find c so that the vectors c4 and 25  are parallel. Let u=c4 and v= 25 be two vectors. Two vectors…

Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Determine the length of each vector.

A:

Q: ors a = 6i + 7j + 6k and b = 4i − j + 8k, where i, j, and k are mutuallyperpendicular unit vectors…

A: In this question, the concept of the dot product is applied. Dot Product The product of the…

Q: a) Show that the three vectors A = 2i – j+ k , B = i - 3j – 5k, Č =-3î + 4j + 4k %3D form the sides…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Find a vector and unit vector perpendicular to each of the vector A + B and A – B,

A:

Q: A. Give the Cross products of the unit vectors (i, j, k).

A: Understanding of cross product of three vectors are required to under this.

Q: 5) Find a unit vector that has opposite direction of the vector i - 2j + 4k.

A: First change direction of vector then find magnitude and write unit vector

Q: In Cª, find a unit vector ū that is a positive real number multiple of z = (1 – i, i, 2, 3+ 4i).

A: Introduction: For a given complex vector z=z1,z2,...,zn, its length is formulated as…

Q: Given the vectors u = -i-5j and v =-3i+2j, find u v

A: Given vectors are  u=-i-5j     and   v=-3i+2j

Q: Show that each pair of vectors is perpendicular.    i + j and i - j

A: Given: u=i+j ,v=i-j

Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

A:

Q: C a

A:

Q: Show that each pair of vectors is perpendicular.     2i + j and i - 2j

A: Solution: Consider the given vectors are  a→ = 2i + jandb→ = i - 2j We know that if the dot product…

Q: Use the given pair of vectors, v= -6i+7j , w= -8j , to find the following quantities. State whether…

A:

Q: Given vectors a, b, c, such that a = 5c + 3d and b = 2c -d, 2a -3b in terms of c and d. express

A: Given vectors, a= 5c+3d b= 2c-d

Q: The vectors a and bare unit vectors such that a a+b and 2a +jb are perpendicular. --Determine the…

A: The given vectors a→ and b→ are unit vectors such that a→.b→=12.Given: a→+b→ and 2a→+jb→ are…

Q: Find the unit vector in the direction of the given vector a, and express it using standard unit…

A: Find the unit vector in the direction of the given vector a . vector a = 20i - 21j  . Here i…

Q: Compute the dot product of the vectors v and w, and find the angle between the vectors. v=−10i+j and…

A: Compute the dot product of the vectors v and w, and find the angle between the vectors. v=−10i+j and…

Q: Given the vector A 2i +3 j, what is 3 A? Expand vector and collect like terms (simplify).

A:

Q: Given nonzero vectors u, v, and w, use dot product and crossproduct notation, as appropriate, to…

A: Let the two vectors be u=u1i+u2j+u3kv=v1i+v2j+v3k

Q: Find a unit vector that is orthogonal to both ı̂ +ȷ̂  and ı̂ +?̂

A: Given query is to find the unit orthogonal vector to the given vectors.

Q: Show that if u+v and u – v are orthogonal, then the vectors u and v must have the same length. If 0…

A: As per our guidelines we are supposed to do only first question among multiple questions. To get the…

Q: Find the vector v and illustrate the specified vector operations geometrically, where u = (−2, 3)…

A:

Q: For any nonzero vector v, the unit vector that has the same direction as v is________ . To find this…

A: For any nonzero vector v, the unit vector that has the same direction as v: To find this vector,…

Q: 8. ABCDEF is a regular hexagon with AB, representing the vector m and AF, the vector n. Find the…

A: Given that: AB→ is representing the vector m and AF→ is representing vector n.

Q: Find two unit vectors in 2-space that make an angle of 45° with 6i + 5j. Enter the vector i as i,…

A: here here we have

Q: Given a vector v with initial point P(5,12) and terminal point Q(−2,−12), write the vector in terms…

A: vector with initial p1,p2 and                 terminal (q1,q2)is given by v=<q1-p1,q2-p2>

Q: B. Find a vector has length 10 in the direction of vector V=.

A:

Q: . Prove: If a and b are both unit vectors, then axb is a unit vector only when a and b are…

A: since you have asked multiple questions in a single request, we would be answering only the first…

Q: For the vectors given here, what are the coefficients in the 123-coordinate system of the tensor B…

A: In order to find B that is the coefficients in the 123 coordinate system,  tensor product of u and v…

Q: Given the three vectors A, B, and D, show that A (B +D) = (A · B) + (A · D).

A:

Q: Given nonzero vectors u, v, and w, use dot product and crossproduct notation, as appropriate, to…

A: It is known that the unit vector along the direction v is given by vv. Since it is an unit vector,…

Q: Assuming vector B is 12 units long, vector 4B is:

A:

Q: express each vector as a product of its length anddirection. 9i - 2j + 6k

A: The given vector is u=9i-2j+6k. Compute the length as follows. u=92+-22+62=81+4+36=81+40=121=11

Q: Express in Cartesian components: (a) the vector at A(4, 40°, -2) that extends to B(5, -110°,2); (b)…

A: express in cartesian components (a) the vector at A4,40°, -2 that extends to B5,-110° , 2 (b) a unit…